I’m a little late to the party on discussing the fouling-up-3 strategy, but for a while I’ve been wanting to interrogate play-by-play data to get a handle on the approach. Not that it matters, but I’ve believed it usually makes sense to foul in these situations and it’s been heartening to see that analysts across the sport have embraced the idea. Contrast that with old-school baseball folks that still struggle accepting that a sacrifice bunt is usually a bad idea despite a large amount of analytical work that backs it up.

While a consensus has formed that fouling is a good idea, there’s always been this nagging piece by John Ezekowitz that has been ignored in these discussions. I’ll admit I was not comfortable with the findings from that piece that indicate playing honest defense has been a more successful approach in the past, but John isn’t one to just go contrarian for the sake of it, so I always thought it should be taken seriously. However, given my nature as a control freak, I’ve wanted to sift through the data myself, and the recent attention given to this issue provided motivation to do that.

I chose to use slightly different assumptions than John. I flagged all possessions at the end of the second half or overtime period where a team trailing by 3 took possession of the ball with between five and 12 seconds left. Then I recorded what happened in that possession (foul/no foul) and whether the game was won or lost by the leading team in regulation, or if the game went to an extra period. The period of record here is every game since the 2009-10 season. First, the results...

Foul cases represent two-shot opportunities, or fewer in the case of a bonus situation. (The flaw in this approach is that there will be the occasional two-shot shooting foul included here. Still, I can justify this a bit because those cases provide a good simulation of truly fouling in that case.) And-ones are assumed to be Defend cases. Foul-3 represents cases where a team was fouled on a three-pointer and shot three free throws. I’ve broken these out in the table above, but like John, I went back and determined which cases occurred as the result of trying to foul, and which cases occurred when trying to honestly defend. Two Three of the 13 cases occurred when trying to foul and both involved an extra period. (The famous Xavier-Kansas State game on 3/25/10, Denver-Arkansas Little Rock on 1/2/11, and Arizona-Florida on 12/7/11 [Updated to add Florida case, 3/1/13]). After cleaning up those cases, this is what the output looks like...

W L OT Win% Cases
Foul 122 5 11 92.0 138
Defend 598 2 76 93.5 676

The winning percentage here is computed as (W+0.5*OT) divided by Cases so no value judgments are made on what happens in the subsequent overtime. The leading team is assumed to have a 50/50 shot to win if the game goes into the extra period. According to my records 48 of the 87 overtime games (55%) were won by the team coming back to tie it. I’m skeptical whether that’s real, but using that figure for OT games, the defenders win 93.4% of the time and foulers win 92.3% of the time.

These results are largely consistent with what Ezekowitz found. Based on my assumptions, defending has surprisingly worked out to be a slightly better strategy over the past three-plus seasons. I’ll try to explain why, but first I think it should be obvious why it might appear that fouling is better. There are 79 cases of something bad happening when a team chose to defend to just fifteen for the foulers. You don’t have to look hard to find cases of a team hitting a three in the closing seconds to force overtime. It happens almost every weekend.

Ben Brust’s heave against Michigan was the latest example of this, and you can’t now re-run the play with Michigan fouling. So all we have is Michigan failing by not fouling. Therefore, people assume fouling is better. (The fact that Michigan had fouls to give complicates the analysis in this case, but some have suggested the Wolverines should have kept fouling before the throw-in until Wisconsin went to the line.) However, we don’t account for the fact that because fouling is attempted so rarely, fouling screw-ups are much more rare in total number.

The other thing is, game-tying shots aren’t losses - they only send the game to overtime. In fact, the chance of an “insta-loss” from defending is remote. It’s only happened twice in 677 cases through last Wednesday, both on four-point plays (Rutgers over Villanova on 2/9/11 and Idaho State over Sacramento State on 1/14/12).

Insta-losses are still rare in the fouling cases, but relatively speaking, they are significantly more likely. (See Appendix A for a complete list of cases since the 2009-10 season.) One of the differences in my study from John’s is that I don’t require the flagged possession to be the last one of the game for the trailing team. This is one of the drawbacks of fouling that needs to be considered and introduces a much higher chance of the insta-loss.

As an example, take the game between the Utah Valley Wolverines and the North Dakota Fightin’ North Dakotans on 1/20/11. NDFND was up 3 and chose to foul UVU late in the 3rd overtime. UVU made both free throws with three seconds left, and then NDFND had trouble inbounding the ball. They called a time-out. They didn’t have any left. UVU made one of the two technicals to force a fourth OT. Now you might say that kind of mistake is preventable with enough practice, but it’s equally true that mistakes happen, and mistakes (both by the players and the officials) need to be considered when implementing a strategy. I might say after NDFND’s blunder, they were lucky to avoid the insta-loss since one of the technical free throws was missed. The possibility, though remote, of an extra possession makes a difference here. (The 11 OT cases after fouling are listed in Appendix B.)

Another reason the fouling strategy isn’t as useful as one would think is that teams really stink at three-pointers when the defense knows they need one and there is a significant time constraint. In the 814 cases studied, teams made 98 out of 608 three-point shots (16.1%) during the possession in question. Basically, assume a player is about half as effective as normal in hitting threes when his team is down three facing a limited clock. He might even be worse since it’s possible these shots were skewed towards more effective shooters.

For all the focus on Brust’s shot, there were 12 other cases that fit my parameters on Saturday. In the ten non-foul cases, teams missed all seven three-point attempts and committed three turnovers - and nobody forced overtime. Focusing on the one case ignores the larger percentages in play here. Michigan was extremely unlucky. (Just to be clear Wisconsin’s possession wouldn’t be included in my study since it started with less than five seconds on the clock. My reason for doing this was to avoid skewing the three-point percentage even lower. Presumably, with five or more seconds left, there’s time to get a better look than Brust did.)

Also, teams are better at getting offensive rebounds on free throws when they absolutely need one and therefore no regard for the opponents getting an easy fast break going the other way. Normally, free throw misses result in about a 15-20% offensive rebounding rate. But in 96 cases of a reboundable free throw in the possessions studied, trailing teams got 39 of them for a rebounding percentage of 40.6. (Each of the 39 cases is listed in Appendix C.)

Throw in those issues along with the possibility of an extra possession, then consider the chances of a foul on a three-pointer in a normal defense, and the historical odds tilt towards not fouling. In fact, I’d also guess that there’s some selection bias in the fouling cases. I'd presume that the cases where the foul option was chosen tend to skew towards optimal situations - the opponents have good three-point shooters or poor offensive rebounders - and even then, fouling can’t be shown to be the best move. It appears that in the average case, it’s better to defend, even if the chances of overtime are higher.

The fact is, chances of losing are close to remote in either case, but execution errors, an inflated offensive rebounding percentage, poor three-point shooting, and the chance of an extra possession are enough to counteract what might otherwise be the advantage of forcing a team to shoot free throws. In cases where the opponent has multiple good three-point shooters and you have confidence in rebounding a missed free throw, fouling may be the better option. But it appears the default decision should be to not foul.

One final note here. Some people might say there’s a definitive conclusion in this. After all, there are over 800 cases. But because there are so few cases of failure, that’s a misrepresentation of the sample size. The fact is, we could use an additional 5-10 years of data before making a definitive statement. Even then, tweaks in the methodology can get you closer to one answer or the other.

However, I think that says something about how difficult it is to determine the proper strategy. To me, the only conclusion one can make is that the criticism of coaches that choose to defend appears to be misplaced. A small percentage of the time you’ll get burned no matter what you choose to do. We will continue to see teams make game-tying threes near the end of games more often than they get fouled simply because more coaches choose this strategy. In the long run, it’s difficult to prove it's a bad idea.

Appendix A: The insta-losses

The stories behind the seven insta-losses since the 2009-10 season are below.

12/21/2009 Arizona over Lipscomb (FOUL): Nic Wise was fouled with five seconds left. He made both, and Arizona subsequently fouled Lipscomb and Adam Hodzic made one of two. Then this happened.

1/4/2010 Florida over N.C. State. (FOUL): N.C. State was up 3 on Florida and fouled with five seconds left. For whatever reason, Erving Walker made both free throws despite Florida being out of time-outs. Florida immediately fouled Javy Gonzalez. Then this happened. I’ll grant you it’s a little unfair to include this in the foul bin, but it was a case where a team chose to foul and insta-lost. In fairness, also please consider the Kansas State-Colorado and Creighton-Iowa State cases in Appendix C where the fouling team was lucky not to insta-lose.

2/13/2010 Cal St. Northridge over Fullerton St. (FOUL): Northridge was up 3 when they fouled Gerard Anderson with four seconds left. Anderson made the first and missed the second. Teammate Eric Williams grabbed the rebound, made a layup and was fouled. He converted the free throw for the 113-112 win.

3/16/2010 Jacksonville over Arizona State (FOUL): With ten seconds left, Jacksonville’s Chris Edwards made two free throws. Jacksonville fouled Derek Glasser, who made one of two free throws with nine seconds left, then Ben Smith hit a three with three seconds left for the 67-66 win.

2/9/2011 Rutgers over Villanova (DEFEND): Jonathan Mitchell was fouled hitting a three for Rutgers with one second left and converted the free throw for a 77-76 win.

1/14/2012 Rice over Tulane (FOUL): Tulane fouled Connor Frizzelle with four seconds left. He made the first free throw, missed the second, and the rebound went out of bounds off of Rice. Frizzelle hit a three at the buzzer for a 50-49 win.

1/14/2012 Idaho State over Sacramento State (DEFEND): Kenny McGowen was fouled hitting a three for Idaho State with eight seconds left. He made the free throw for the 68-67 win.

Appendix B: OT cases after fouling

There were 11 12 cases where a fouling team went to OT.

2/11/10 Northern Arizona-Idaho State: NAU’s Julian Olubuyi went to the line with six seconds left, made the first, missed the second, and the rebound went out of bounds off Idaho State. DeAngelo Jones converted a layup to force overtime.

3/14/10 Kentucky-Mississippi State: Maybe the most famous case of the fouling strategy backfiring. Eric Bledsoe had two free throws with three seconds left, made the first, missed the second, and overtime was forced on a Demarcus Cousins put back of a John Wall miss. (Video)

3/25/10 Xavier-Kansas State: With K-State trying to foul Xavier, Terrell Holloway was able to launch a three as the whistle sounded with 5.0 seconds left. He made all three free throws to force overtime.

1/1/11 Milwaukee-Detroit: Milwaukee’s Tone Boyle was fouled with five seconds left and made both free throws. Milwaukee promptly fouled Ray McCallum, who made both of his free throws. Milwaukee’s Kaylon WIlliams responded with a 30-footer at the buzzer to force overtime.

1/2/11 Arkansas Little Rock-Denver: With 4.4 seconds left Denver tried to give a foul, but UALR’s Solomon Bozeman launched a shot on the whistle and got three free throws. He missed the first and made the next two. UALR then fouled Denver’s Travis Hallam with 2.6 seconds left and he made both free throws. After a wild throw-in that went out of bounds off Denver, UALR’s Alex Garcia-Mendoza hit a contested three at the buzzer to force overtime. (Video)

1/20/11 Utah Valley-North Dakota: Described in the main article

2/19/11 Tulane-Marshall: Tulane’s Trent Rogers was fouled with 3.2 seconds left. He made the first, missed the second, but Marshall’s DeAndre Kane traveled after grabbing the rebound. On the subsequent inbounds, Rogers was fouled on a three-point attempt and made two free throws to force overtime.

12/1/11 IUPUI-South Dakota State: IUPUI’s Sean Esposito was fouled with five seconds left. He made the first, missed the second, but teammate Alex Young grabbed the rebound. He was fouled on his putback attempt and made both free throws to force overtime.

12/7/11 Arizona-Florida: Casey Prather fouled Solomon Hill, who "flailed his arms" to draw a shooting foul. Hill made all three free throws to force OT.

12/19/11 Colgate-Dartmouth: Colgate’s Mitch Rolls was fouled with 3.5 seconds left. He made the first, missed the second, but teammate Sterling Melville grabbed the rebound and was fouled with 2.7 seconds left. He made both free throws and forced overtime.

11/18/12 Valparaiso-Kent State: Valpo’s Erik Buggs was fouled with four seconds left. He made the first, missed the second, but Kevin Van Wijk got the rebound and converted the put-back to force overtime.

1/24/13 Troy-Arkansas State: Troy’s Antoine Myers was fouled with six seconds left. He missed the front end of the one-and-one, but the rebound went out of bounds off Arkansas State. Emil Jones made a three with 1.7 seconds left to force overtime.

Appendix C

Listed here are the 39 cases where a missed free throw was rebounded by the offense in foul situations. (Rebounding/trailing team listed first, * indicates team was successful in tying or leading game but still lost in regulation on subsequent possession, ** indicates team attempted 3-pointer after the offensive rebound.)

11/12/10 Samford**-Youngstown State
11/14/10 Sacramento State-Cal St. Bakersfield
11/21/10 Creighton*-Iowa State (Creighton tied the game after Antoine Young rebounded his own missed free throw and made two free throws after being fouled again. Iowa State’s Jamie Vanderbeken responded with a 30-footer at the buzzer to preserve the win for Iowa State. However from the video, the shot appears to be launched after the buzzer. The game was not televised so there was not an opportunity to review it.)
12/20/10 UNC Wilmington**-Illinois State
12/22/10 Colgate-Albany
1/1/11 New Mexico**-Dayton
1/27/11 Iona-Rider
2/12/11 Kansas State***-Colorado (The triple asterisk here was because K-State did shoot - and make - a three-pointer after the offensive rebound, which was ruled good. But a replay review overturned the call. Recap.)
2/13/11 Sacramento State-Montana State
2/19/11 La Salle - George Washington
3/10/11 Washington State-Washington
3/11/11 Grambling-Jackson State (OT)
3/18/11 Memphis-Arizona